Even a £20m England international with 34 caps needs a clear sense of direction in his game.

Steven Gerrard's blindside run showed Stewart Downing where to deliver his first Premier League assist for Liverpool. The basic errors that still litter John Arne Riise's defending presented the way to his first league goal since leaving Aston Villa 17 months ago. And being informed his Liverpool career was in effect ending in January may, just may, have rescued it.

Downing was the stand-out player of an exemplary Liverpool performance against a sorry Fulham team – with the exception of Dimitar Berbatov – that are destined for a fraught struggle for survival. The calibre of the opposition should not detract from Downing's recovery at Anfield, however. He was Liverpool's best player in the preceding defeat by Villa, while out of position at left-back, and there has been improvement in each of his seven starts in the last eight games. The reason? As the 28-year-old admits with brutal honesty, he had to attract a new club.

As an expensive recruit under Kenny Dalglish, and one who concedes he has lacked consistency since the move from Villa, Downing's face and salary has not appeared to fit with Brendan Rodgers's designs for Anfield. The Liverpool manager told the midfielder to look elsewhere in January if he could not cement a place in a team short on options and experience. "If he keeps playing like that he is going nowhere," was Rodgers's position on Saturday.

Downing said: "After our conversation I just thought: 'I have to go for it.' I had nothing to lose. It looked as though I would be on my way in January so basically I had to play well to get a new club. It seems to be coming together now and I am pleased. It has been hard work at times but you have got to keep persevering, stay strong, and I got my reward against Fulham.

"Being told I could go was a kick up the arse. The moment that happens you are playing for a new club and looking for a move, while trying to play well at the same time. It seems to have gone well but I have never wanted to leave Liverpool. But it was out of my hands. The only thing I could do was play well and try and make the manager change his mind."

The England midfielder only heard of Rodgers's reappraisal as he was walking out of Anfield on Saturday night. "If he wants me to stay now that just shows how quickly things can change in football," said Downing, with an element of surprise that was surpassed when Rodgers initially announced he could leave.

Downing said: "The manager was pleased with me at the start but then things changed very quickly and I was told I could go. I don't know who makes that decision but one minute I was told I was doing well and the next I was told I could go, so it was a bit confusing.

"It was confusing that I was in the team and then I was told I could leave but all a footballer can do in that situation is try to change the manager's mind. If it was a gee-up for me to tell me I could go, if it was meant to be a kick up the arse, then maybe it has worked because the performances are coming now and hopefully it continues.

"I want to stay. I never wanted to leave but obviously I was out of the team, I was frustrated as a result of that, and in that situation you have to look at something if it crops up. The only thing I can do is play well and make him keep me here. I am pleased it has come together because I have worked hard to get to a club like this and I don't want to leave in a hurry."

Liverpool were in a rush to remedy mistakes against Villa too. A dominant start on this occasion produced an early goal as Martin Skrtel converted Gerrard's corner with a finish unusually composed for a central defender. The breakthrough was not the only contrast with the Villa defeat as Fulham's makeshift central midfield gave Gerrard licence to control the flow and their lack of conviction once behind, and lack of quality, was marked. Gerrard ended the contest with a low finish from Downing's exquisite pass before, with Anfield expectant, the winger was shown on to his stronger foot by Riise and beat Mark Schwarzer convincingly.

Fulham would have been flattered by 3-0. In stoppage time Luis Suárez converted José Enrique's cut-back from the byline to provide a more accurate reflection of Liverpool's superiority.